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Last update: Mgr. Kateřina Mikšová (23.04.2018)
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Last update: doc. RNDr. Mirko Rokyta, CSc. (28.10.2019)
Kopáček, J. a kol.: Matematika pro fyziky, díly II-IV, skriptum MFF UK |
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Last update: doc. RNDr. Mirko Rokyta, CSc. (01.10.2017)
1. Eigenvalue and eigenvector of a matrix
• Eigenvectors, eigenvalues and characteristic polynomial
• Jordan canonical form
2. Ordinary differential equations (ODE's)
• nth order ODE's, it's connection to 1. order ODE's
• linear ODE's , fundamental system
• the method of characteristic polynomial, variation of constants
• the Euler equation, differential equation in the shape of the total differential
3. The sequences and infinity sums of functions
• Pointwise and uniform convergence
• Demonstration of basic problems connected to the change of limit and sum, limit and
derivation, integral and sum, integral and limit.
4. Fourier series
• Fourier trigonometric series. The convergence of Fourier series
• Bessel inequality a Parseval equality
5. Hilbert spaces,
• Hilbert space, orthogonal systems and completeness,
• abstract Fourier series, abstract Bessel inequality and Parseval equality
• Orthogonal systems of polynomials: Legendre, Laguerre, Hermite, Tsebysev apod.
6. Complex analysis
• Complex integral, primitive functions.
• Cauchy formula
• Taylor and Laurent series.
• Residue theorem a its applications. |